A number of partially and/or completely non-elucidated problems arise in any theory. If these problems are confirmed in practices, they are enounced as a ‘laws’ and after ‘forgotten’. In the following, I had tried to analyze some of these problems.
About Cannon Bullet Trajectory
Two solutions exist for the mathematical model of a cannon bullet trajectory fired through a given angle α. In Cartesian coordinates and the X-Z plane these equations of the trajectory are:
(1) where
is the projection on the ground of the trajectory,
is the projection of the trajectory on a vertical of the ground,
is the initial speed of the bullet,
the time,
the time when the bullet was fired and
the earth gravitational acceleration. Solving this system, it results:
(2) which is the equation of a parabola. The trajectories corresponding to this equation may be obtained to eliminate the ‘
t’ variable. Two solutions are obtained (Figure 1 and Figure 2):
(3)For 
, 
, 
it results:
(4)Figure 1. Bullet trajectory corresponding to the first solution
Figure 2. Bullet trajectory corresponding to the second solution
It can be observed that the first solution corresponds to a correct physical situation but not the second solution. Let now consider that the second solution correspond to the antipodes of the earth of the first solution. In this case, 
, 
. 
and it results:
(5)The corresponding trajectory to the relation 5 can be shown in the Figure 3. Symbolically, both solutions are represented in Figure 4 where each solution correspond only to the given parameters and position of cannon on the earth.